Well theres more material to work with now right?
With GL, it wasnt based on anything and essentially ran its course.
Heres to hoping for source material following Ao no.
I mean were already getting new D. grey-man, so why not?

The professor sat down, utterly defeated by the young man's overwhelming brilliance.
That young man’s name?
Albert Einstein.

A potential issue I always saw was with how they ended things in the tv adaptation, basically Yukio going all demon and what not, and all that other shit; giving him tail and ears and stuff. I know in the manga they are hinting there's more to him, but the show completely jumped the gun on him.

If they do continue the series I really hope they just act as if all that crap didn't happen and they just go on from the last canon moment.

One would hope...
A non-canon ending usually is pretty awful.
I cant actually think of a non-canon, anime only, ending that was NOT awful now that I think about it.

The first season of Noragami did it kind of decently.

A problem I see a lot of series make is once they run out of material they pretty much finish off the story in a way which kills any chance of it continuing, them doing something that goes against the series. With Noragami the material the first season covered barely had anything to it, them creating the villain Rabo I think his name is, he didn't do anything to alter the series or change what it would be, him simply being someone they needed to fight. Them leaving the true story untouched, vs other series that put their hands all over a series and make it go in a direction that goes against what happened before. I still hated Rabo a lot though, him feeling very mary sue like, him being like someone out of fanfiction, him being placed as someone that knew the main character deeply long ago and worked with him.

Ideally, they redo the series entirely instead of trying to continue and act like the first one never happened.

There really isn't a need to do something like that. The series did have much padding, like that cooking demon, and a few things now and then, however it didn't take away from things.

If they were to do a redo of sorts, they could just make a movie adaptation, kind of like the gurren lagann movies in which they condense most of the series into a 2 hour max movie, them cutting out the padding from the anime, and at the end of it, have it end the proper way leading into the new series.

Even the last bit that was canon was bastardized in my opinion, the anime being the one that had Rin's sword break and need his friends to go repair it, and there's also how when it came to Rin's trial, in the manga he was fully conscious and aware for his trial, but in the show they did something stupid by having him frozen in a crystal, hovering over everyone.

That's why it would be easier for them to redo the series instead of trying to act like the filler events of the first series never happened. It would let them correct some mistakes that were made, which I always prefer over them trying to retcon with a continuation.

They've got enough material to work with, but they'll have to pretend the filler never happened like Book of Circus because they made an effort to make sure they couldn't do something as simple as carry on with the source material from where they left off.

Additionally, popularity would be a major determining factor on if there'll be a season 2. Can't vouch for readership, but I'd imagine it's not as popular as it was in 2011, so the likelihood will be that they might be trying to gauge the series' popularity to see if a 2nd season would be successful.

The only accurate way to really gauge interest would be to give an honest attempt, like I said about making a movie adaptation, condensing things down and correcting parts. If they just release a pac***ko machine and use feedback from that to determine if they should continue the series, that would be pretty bullshit. Considering I'm pretty sure the same people that go for pac***ko machines aren't in the same crowd as those that watch anime.

Hopefully, they will give Blue Exorcist another season. It already feels like an incomplete series. If they do make another season, I hope they do more exploring with Renzo Shima. Even though I'm not a Manga reader, I have read summaries about Shima being something along the lines of a double agent.

"Revenge can be bittersweet, but if you sit back and watch, KARMA can be pure entertainment." ~ David Avocado Wolfe

"If a guy wants you for your breasts, thighs, and legs, send him to KFC. You're a lady, not a cheap value meal." ~ Nicolas Cage